Prove that the curves `y=x^(3) and xy-k` cut each other orthogonally, if 3k= 1.

Prove that the curves 2y^(2)=x^(3) and y^(2)=32x cut each other orthogonally at the origin

Prove that the curve y=x^(2) and xy=k intersect orthogonally if 8k^(2)=1

Prove that if the curves y=x^(3) and xy=K intersect orthogonally,then 3K=1

Prove that the curve y = x^2 and xy = k intersect orthogonally if 8k^2 = 1 .

Show that the curve x^(3)-3xy^(2)=a and 3x^(2)y-y^(3)=b cut each other orthogonally, where a and b are constants.

Prove that the curves x = y^(2) and xy = k cut at right angles, if 8k^(2) = 1 .

Show that the curves 2x=y^(2) and 2xy=k cut each other at right angles if k^(2)=8

Prove that the curves x = y^(2) and xy = k cut at right angles* if 8k^(2) = 1 .

Prove that the curves x = y^(2) and xy = k cut at right angles* if 8k^(2) = 1 .

Prove that the curves x = y^(2) and xy = k cut at right angles* if 8k^(2) = 1 .